Non-linearity and EFA

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Non-linearity and EFA
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Single component elution in HPLC-DAD system
20 non-linearity
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Ideal
Non-linear
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Spectra in two dimensional wavelength space
475-500 nm
Ideal
Non-linear
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Spectra in two dimensional wavelength space
495-500 nm
Ideal
Non-linear
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Evolving Factor Analysis (EFA)
Ideal
Non-linear
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Evolving Factor Analysis (EFA)
Ideal
Non-linear
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Embedded elution and EFA
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Consecutive elution
tm1 40, tm260
w1 11, w28.5
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HPLC-DAD data
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Ebedded elution
tm1 50, tm257
w1 12, w26.5
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HPLC-DAD data
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EFA
Consecutive elution
Embedded elution
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EFA
Consecutive elution
Embedded elution
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The main assumption of EFA is that the component,
which appears first, will disappear first. Indeed
it is often but not always the case for
sequential elution.
The main question is which end belongs to which
start?
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Exhaustive Evolving Factor Analysis
E-EFA analyzes all possible sub-matrices of the
measured matrix, which are combined by the two
outsides submatrices of a selected window, and an
apparent difference is found between the similar
results that are obtained by the traditional EFA.
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 1
Rank 1
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Exhaustive Evolving Factor Analysis
Rank 0
Rank 0
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 2
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 1
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 1
Rank 2
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Exhaustive Evolving Factor Analysis
Rank 1
Rank 1
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Sectional Moving Window Factor Analysis (SMWFA)
is a fast, friendly and useful for automatic
resolution of hyphenated chromatographic data.
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Sectional Moving Window Factor Analysis
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SMWFA.m file For sectional moving window factor
analysis of two component systems
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Use the SMWFA.m file and investigate the effects
of noise values on HPLC-DAD data in embedded
elution systems.
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Rank Deficiency and EFA
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Rank deficiency in a system with two independent
chemical processes
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HB B- Ct2
Ct1 a Ct2
HA A- a (HB B-)
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Augmentation

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1 2 3
3 2 1
2 4 6
6 4 2
1 2 3
3 2 1
0 0 0
0 0 0
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1 2 3
3 2 1
4 4 4


1 2 3
3 2 1
4 4 4
2 4 6
6 4 2
8 8 8


0 0 0
0 0 0
0 0 0
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pKa14
pKa2.5
pKa26
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Forward and backward eigen analysis
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EFA Results
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standard
Augmentation
mixture
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standard
mixture
Forward Analysis
standard
mixture
Backward Analysis
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Forward and backward eigen analysis
standard
mixture
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EFA Results
standard
mixture
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Concentration Profiles
standard
mixture
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mixture
Augmentation
standard
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standard
mixture
Forward Analysis
standard
mixture
Backward Analysis
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Forward and backward eigen analysis
standard
mixture
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EFA Results
standard
mixture
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Concentration Profiles
standard
mixture
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standard
mixture
Forward Analysis
standard
mixture
Backward Analysis
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Forward and backward eigen analysis
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Forward and backward eigen analysis
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Mixture of H2A and H2B
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H2A
pKa12
pKa23
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H2B
pKa14.5
pKa26.5
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EFARD.m file EFA on data with rank deficiency
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Outputs of EFARD.m
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Outputs of EFARD.m